No, the MC3PHAC would not be able to drive that motor. The MC3PHAC is designed for AC induction motors (think "washing machine"), and not for permanent-magnet motors. Also, the MC3PHAC is meant to drive motors at AC line voltages, and the motor you linked to is a low voltage / high-current battery-powered motor.

There are different ways to drive that motor, depending on the application. If you are driving a model aircraft propeller, as the motor was designed, then a single mosfet switched from some PWM controller would be appropriate (that would be "single-quadrant" operation). Other applications might need two or four quadrant operation. If you need precise speed regulation, or position control, then that motor may be a bad choice.

There is no way to drive a brushless motor with a "single mosfet". I was thinking of a brushed motor when I wrote that. Sorry.

The datasheet does not help in determining how many transistors you will need. If it is wired in a "wye" configuration with a center-tap (four wires), then you can get away with three switches. But more likely it is wired in a "delta" configuration (three wires), which means you will need six switches. Whether those switches are bipolar transistors or mosfet transistors would depend on the amount of current it will typically draw.

The hard part will be the commutation (knowing when to switch windings). That particular motor has no feedback, except for its back-emf. There may be ICs that can commutate using back-emf (it's not a difficult process), but I have not seen one. I have always used a DSP to do that.